Nonequilibrium Green’s function approach to strongly correlated few-electron quantum dots

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's function theory. The ground and equilibrium states are self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second-order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for the zero and finite temperature charge carrier densities, the orbital-resolved distribution functions, and the self-consistent total energies and spectral functions for isotropic two-dimensional parabolic confinement as well as for the limit of large anisotropy---quasi-one-dimensional entrapment. For the considered quantum dots with $N=2$, 3, and 6 electrons, the analysis comprises the crossover from Fermi gas or liquid (at large carrier density) to Wigner molecule or crystal behavior (in the low-density limit).